Question

escreva na forma trigonométrica z=3-3i​

Answer 1

Resposta:

Explicação passo-a-passo:

Z = 3 - 3i, a = 3 > 0  e b = -3 < 0, indica que alfa pertence ao 4° quadrante.

$P = \sqrt{a^{2}+b^{2}}\\\\ P=\sqrt{3^{2}+(-3)^{2}}\\\\P=\sqrt{9+9} \\\\P=\sqrt{9.2}\\\\P=3\sqrt{2}\\\\cos\alpha = \frac{a}{P}\\\\cos\alpha=\frac{3}{3\sqrt{2} }\\\\cos\alpha=\frac{1}{\sqrt{2} }\\\\cos\alpha=\frac{\sqrt{2} }{2}\\\\sen\alpha=\frac{b}{P}\\\\sen\alpha=-\frac{3}{3\sqrt{2}}\\\\sen\alpha=-\frac{1}{\sqrt{2}}\\\\sen\alpha=-\frac{\sqrt{2} }{2}\\\\\\\alpha=2\pi- \frac{\pi }{4} \\\\\alpha=\frac{7\pi }{4}\\\\ Z=P(cos\alpha+isen\alpha)$$Z=3\sqrt{2}\:(cos\frac{7\pi }{4} +isen\frac{7\pi }{4})$